The problem of gas bubbles propagating in confined capillary channels has been the subject of extensive theoretical, experimental, and numerical investigation (see [1]} and references therein). In addition to being a classic problem in fluid mechanics, as seen in the now-seminal works of [2]}, [3]}, [4]}, these flows are central to multiple applications in technology development and are found in several real-life systems. To name a few examples, gas-liquid interfaces in the micro- and capillary scale are involved in two-phase coolers [5]}, \({\rm CO}_{2}\)  sequestration and storage microdevices [6]}, obstructed pulmonary airways [7]}, and volcanic conduits [8]}, and have been proposed as a potential method for bacterial detachment and cleaning [9]}. Since the early works mentioned above, extensive efforts have been undertaken to understand the phenomena dictating the bubble's behaviour along with the surrounding thin liquid film, largely through an idealisation of the operating conditions and the morphology of the bubble itself as a flat cylinder bounded by two semi-spherical menisci. It is well-known by experiments [2]} and theory [3]} that the film thickness of the flat region scales as \(h \sim Ca_{b}^{2/3}\)  within the realms of vanishing capillary, \(Ca_{b}\) , and Reynolds numbers, \(Re_{b}\) , and as \(h \sim Ca_{b}^{2/3}/(1+Ca_{b}^{2/3})\)  for \(Ca_{b} < 2\)  [12]}, [13]}. As inertial effects become non-negligible, [14]} proposed a correction to the scaling exponents of \(Ca_{b}\)  and the introduction of the Weber number, \(We_{b}\) , in the scaling law expression. Particular attention has also been placed on exploring the influence of \(Ca_{b}\)  on the pressure drop ahead of the bubble [15]}, mapping the full bubble topological profiles [16]}, analysing the undulatory structures that emerge in the vicinity of the bubble rear [17]}, [18]} as inertial effects begin to dominate, and predicting the final shape of the front meniscus [19]}.
